No. XCV

Circles

The second diagram shows how this figure is arrived at, by drawing three similar and intersecting circles, which have their centres at the angles of an equilateral triangle. The piece cut off by the dotted line corresponds to the section that completes the circle below.

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The catch-words Cleans, Scrubs, Scours, Polishes, which proclaim the merits of an “Old Dutch Cleanser” on the sails of this windmill,

Windmill

can be recast so that the same letters form the singularly appropriatesentence—

“O rub on, sir, success spells cash!”

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The following diagram shows the solution of this new chess puzzle, and fulfils its conditions that no Queen should attack a Queen, no Rook a Rook, no Bishop a Bishop, and no Knight a Knight.

Image

Mr Dudeney explains that only 8 Queens or 8 Rooks can be thus placed upon the board, while the greatest number of Bishops is fourteen, and of Knights thirty-two. But as all Knights must be placed on squares of the same colour, while the Queens occupy four of each colour, and the bishops seven of each colour, it follows that only twenty-one Knights can be placed, and the arrangement shown above contains the maximum number of these pieces under the conditions.

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This diagram shows the order in which the syllables or words of the eight-line verse are to be read on the course of a Knight’s moves atchess—

Image

They runthus:—

The man that hath no love of chess,Is, truth to say, a sorry wight;Disloyal to his King and Queen,A faithless and ungallant Knight.He hateth our good mother Church,And sneereth at the bishop’s lawn;May bad luck force him soon to placeHis castles and estates in pawn!

The man that hath no love of chess,Is, truth to say, a sorry wight;Disloyal to his King and Queen,A faithless and ungallant Knight.He hateth our good mother Church,And sneereth at the bishop’s lawn;May bad luck force him soon to placeHis castles and estates in pawn!

The man that hath no love of chess,Is, truth to say, a sorry wight;Disloyal to his King and Queen,A faithless and ungallant Knight.He hateth our good mother Church,And sneereth at the bishop’s lawn;May bad luck force him soon to placeHis castles and estates in pawn!

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If such a network as is shown in the diagram below is drawn on clear tracing-paper and placed on the page of a book, it will conceal the words beneath it.

Grid

But if, while lying close to the page, it is moved quickly round and about, the letters and words will be distinctly seen, just as objects on the other side of close lattice-work become visible as we pass them quickly in a train.

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These are the results of cutting, in the direction of the dotted lines, completely round a simple paper ring, a ring with one twist, and a ring with a double twist.

Rings

We have (1) two simple rings; (2) one large-twisted ring; (3) two rings linked together. If a third twist is given before cutting, a curious knot is formed.

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The string when it has been placed in the position shown in the diagram, and two buttons larger than the hole have been fixed upon its ends can be easily removed if the narrow slip of the leather is drawn through the hole.

Buttons

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The scissors, when securely fastened, as is shown in the diagram,

Scissors

can be easily released by passing the loop upward through the handle, and then completely over them.

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The primitive wolf-trap consisted of two circular fences higher than a wolf could scale, with a gate as was shown on the former diagram. To set the trap a lamb was placed in the safe centre, and the gate was opened as is shownbelow—

Wolf trap

Attracted by the bleating of the lamb, the wolf entered the outer circle, made his way round, and presently pushed aside the gate, which closed with a spring, and shut off all escape.

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When you have told someone to think of a number between 5 and 15, and while you are not looking, to count upwards from the lowest card step, and round in the direction indicated by the arrow, until that number is reached, and then, starting afresh with “one” on that card to count backwards round the semi-circle, this timenot including the central upright or the steps below it, until the number thought of is again reached,you can tell at once which is the final card arrived at, for it will be as many placesupwards on the leftas there arestep cards and their upright.

Dominoes

Thus if there are 3 steps, it must always be the fourth card upwards on the left of the semi-circle. To keep up the puzzle, the number of steps should each time be changed, on the pretext that their number does not signify.

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This diagram shows how the apple may be divided into six pieces by two straight cuts, so that there shall be a gash in each piece.

Apple

First cut the apple through the dotted line, then place the upper piece shown at the side of the larger piece, and make the second cut straight through, where the line is drawn.

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The sixpence under the middle of the tumbler can be easily removedthus—

Glass

Slip larger coins under opposite edges of the tumbler to raise it slightly, and then scratch firmly on the cloth, from just outside the rim, in the direction you wish the sixpence to take. It will at once respond, and makes its own way gradually outside the circle that had surrounded it.

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This is the way to draw thespiral—

Spiral

Tie a piece of strong thread with a loop at its end round the upper part of the windings of a screw. Drive the screw into a board, through the middle of a card, wind the thread down the screw so that its loop just reaches the card, place a pencil in this loop, and draw the spiral freely, unwinding the thread from the grooves of the screw, and keeping it always taut. A perfect spiral is the result.

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The secret of the talking head is simple indeed when you know it.

Talking head

Between the front and two side legs of the table mirrors are fixed, which reflect the similar surroundings, so that the performer, kneeling behind these, and putting his head through a hole in the table top, completely conceals his body and limbs from the audience.

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The picture charade is completedthus—

Puffin

My first may blow the candle out,My second then comes in;My whole in water moves aboutWithout an oar or fin—

My first may blow the candle out,My second then comes in;My whole in water moves aboutWithout an oar or fin—

My first may blow the candle out,My second then comes in;My whole in water moves aboutWithout an oar or fin—

and is solved byPuffin.

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When the walnuts and cobnuts have been arranged as is shown on thediagram—

Nuts

they can be shifted so that they stand alternately, by moving two that are close together at a time, in four moves, asfollows:—

(1) Move 2 and 3 beyond 8.

(2) Move 5 and 6 between 1 and 4.

(3) Move what are now 6th and 7th in the gap.

(4) Move what are now 1st and 2nd in the gap, and the alternate arrangement is complete.

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The question suggested by this picture riddle is: Why is a waiter like a racehorse? And the solution is: Because he runs for cups and plates.

Riddle

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